Answer:
£160,000
Step-by-step explanation:
Alice bought the house in 2008 for £x.
In 2014, the house sold for a 20% profit, so it sold for 1.2x. (* see explanation below)
In 2019, the house sold for a 5% loss, so it sold for 0.95(1.2x). (* see explanation below)
In 2019, it sold for £182,400.
0.95(1.2x) = 182,400
1.14x = 182,400
x = 182,400/1.14
x = 160,000
Answer: £160,000
* Explanation of 1.2 and 0.95.
A quick way to apply a percent increase or decrease to a number is to using the following method. The number you start with is 100% of the number. If you are adding a percent to it, then add the percent to 100% and convert it to a decimal. If you are subtracting the percent, then subtract the percent from 100% and convert to a decimal. Then multiply the decimal by the original number to find the increased or decreased number.
Example of percent increase:
A book used to cost £10. The price went up by 12%. What is the new price?
100% + 12% = 112% = 1.12
1.12 * £10 = £11.20
Example of percent decrease:
A pair of trousers costs £60. It is on sale at 35% off the regular price. What is the sale price?
100% - 35% = 65% = 0.65
0.65 * £60 = £39
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